Projection screens are commonly fabricated by those skilled in the art either from fiberglass laid up over a mold, or from panels of aluminum sheet supported by a structure of ribs and trusses. In the case of a fiberglass ellipsoidal screen, a mold must be created for the entire segment surface, with constantly varying surface curvatures. This type of mold is expensive to create and inspect.
In the case of an aluminum screen, each panel is limited in size to a maximum of 4 feet by 12 feet, this being the standard size for aluminum sheet. For common projection surfaces like spheres and tori, all panels may be press-formed from the same die. The panels are then cut along lines of latitude and longitude of the sphere or torus and placed on a framework that supports the panels in close juxtaposition, such that the interior surface of a portion of a sphere or torus is created. The use of a single die is an important feature of the process, as the non-recurring cost of fabrication of such a die, commonly made by those skilled in the art from epoxy or laminated maple, may be the same as the recurring cost of an entire screen.
For the manufacture of an ellipsoidal segment described by the prior invention, however, fabrication of each segment from a plurality of panels, such that the size of any panel does not exceed the aforementioned limited size, requires the use of not one but four dies: one for the left panel, one for the left center panel, one for the right center panel, and one for the right panel. While the left-right inner and outer pairs are mirror images of one another, this accrues to no advantage in reducing the unit cost of the dies. Therefore, the tooling cost of the ellipsoidal segmented screen is several times greater than that of the simpler spherical or torus screen, and this cost is a significant portion of the total cost of one or several screens.
It would be desirable, therefore, to approximate the ellipsoidal shapes of screen segments of a segmented ellipsoidal screen using the simpler surface of a torus, presuming that the torus could be specified so as to preserve the worthy attributes of the high-gain segmented ellipsoidal screen, to wit, the absence of discontinuities in brightness across channel boundaries when viewed from a point away from the center eyepoint and high overall brightness.